Mathematics - Application of Derivative Question with Solution | TestHub

$f^{\prime }(x)=2\cos 2x-1$; $f^{\prime }(x)=0$ if $x=-\frac{\pi }{6},\frac{\pi }{6}$

$f^{\prime }(x)>0$ if $x\in \left(-\frac{\pi }{6},\frac{\pi }{6}\right)$

$f^{\prime }(x)<0$ if $x\in \left[-\frac{\pi }{2},-\frac{\pi }{6}\right)$ or $x\in \left(\frac{\pi }{6},\frac{\pi }{2}\right]$

Max $f=\max \left\{f\left(-\frac{\pi }{2}\right),f\left(\frac{\pi }{6}\right)\right\}=\max \left\{\frac{\pi }{2},\frac{\sqrt{3}}{2}-\frac{\pi }{6}\right\}=\frac{\pi }{2}$

Min $f=-\frac{\pi }{2}$ since $f$ is an odd function.